Topic 5.2 Calculations of enthalpy changes Energetics Topic 5.2 Calculations of enthalpy changes

Calorimetry Calorimetry- defined as the measurement of heat changes. Specific heat (s) – the amount of heat necessary to raise the temperature of 1 g of a substance by 1 oC. Heat capacity (C)- the amount of heat required to raise the temperature of a given quantity of a substance by 1 oC. So, C = m· s

Calorimetry The heat(q) that is absorbed or released in a given process can be calculated by the following equation: q= m · s · ΔT ΔT= T final – T initial Substances with large specific heats require more heat to raise their temperature. Since C = m· s, the amount of heat absorbed or released can also be defined as: q= C x ΔT

Calorimetry Examples: 1. How many joules are required to heat 352 g of water from 32 to 95 degrees Celsius?

Calorimetry 2. If we add 450 cal of heat to 37 grams of ethanol (specific heat= 0.59 cal/g oC), at 20 degrees Celsius, what would be the final temperature?

Calorimetry According to the law of conservation of energy, if an object is dropped into a cold object, or vice versa, the heat given up by the hot object is absorbed by the cold object; this can be expressed as follows: qlost=qgained qhot = qcold + qcalorimeter (q= m · s · ΔT)hot = (q= m · s · ΔT)cold + (C ∙ ΔT) This equation can be used to find the specific heat of an object. The specific heat of an object can be obtained by placing the object in a known amount of cold water at a known temperature. The specific heat of water is 1.00 cal/g∙oC or 4.184 J/g ∙ oC

Calorimetry For example, an unknown metal with a mass of 35.542 g is heated to 95.0 degrees Celsius and placed in a beaker of water with 75.123 g of water at 25.0 degrees Celsius. The temperature of the water rises to 39.0 degrees Celsius. What is the specific heat of metal?

Constant Pressure Calorimetry Constant pressure calorimeter - a device used for determining the heat transfer for a variety of physical and chemical processes (except in combustion reactions) under constant atmospheric pressure. To express the heat that is transferred under constant pressure conditions, we use the symbols qp or ∆H (pronounced delta H or enthalpy change).

Enthalpy Changes of Reaction in Solution The enthalpy changes of reaction in solution can be calculated by carrying out the reaction in an insulated system, for example, a polystyrene cup. The heat released or absorbed by the reaction can be measured from the temperature change of the water.

Enthalpy Changes of Reaction in Solution The heat capacity of a coffee cup calorimeter can be determined by pouring an known amount of hot water into a known amount of cold water in the following manner: q lost = q gained q hot water = q cold water + q cal (m x s x ∆T)hot water = (m x s x ∆T)cold water + (C x ∆ T)cal After rearranging the equation above, C cal can be obtained as such: Ccal = (m x s x ∆T)hot water - (m x s x ∆T)cold water / ∆ Tcal

Enthalpy Changes of Reaction in Solution Example: When 49.787 g of water at 64.5 oC is poured into 50.045 g of water at 24.2 oC contained in a coffee cup calorimeter, the temperature rises to 43.5 oC. Given this information, what ist he heat capacity of the calorimeter (in cal/oC)? Specific heat of water is 1.00 cal/g∙oC.

Enthalpy Changes of Reaction in Solution To find the enthalpy change that occurs during a reaction, determine the heat change that occurs in the solution where the reaction takes place. q rxn= q solution q rxn = (m x s x ΔT)soln Divide the heat of reaction by moles of reactant to obtain the enthalpy of the reaction in kJ/mol.

Enthalpy Changes of Reaction in Solution Example 50.0 cm3 of 1.00 mol dm-3 hydrochloric acid solution was added to 50.0 cm3 of 1.00 mol dm-3 sodium hydroxide solution in a polystyrene beaker. The initial temperature of both solutions was 16.7oC. After stirring and accounting for heat loss, the highest temperature reached was 23.5oC. Calculate the enthalpy change for this reaction. q neutralization rxn= q solution

Enthalpy Changes of Reaction in Solution Step 1- write equation for the reaction HCl(aq) + NaOH(aq)  NaCl(aq) + H2O(l) Step 2- Calculate molar quantities Mol HCl = 50.0/1000 x 1.00 = 0.0500 mol Mol NaOH = 50.0/1000 x 1.00 = 0.0500 mol Therefore, the heat evolved will be for 0.0500 mol Step 3- Calculate the heat evolved Total volume of solution = sum of both solutions 50.0 + 50.0 = 100.0 mL solution Mass of solution – assume density of solution is the same as water, so 100.0 mL = 100.0 g solution

Enthalpy Changes of Reaction in Solution Specific heat of solution = assume specific heat of solution is the same as water = 4.184 J/g oC q neut = (m x s x ΔT)soln q neu = 100 x 4.184 x 6.8 = 2.84 kJ Δ H = - 2.84 kJ /0.0500 mol = -56.8 kJ mol-1 The negative value indicates that this reaction is exothermic.

Enthalpy Changes of Reaction in Solution One of the largest sources of error in experiments conducted in a polystyrene cup is heat losses to the environment. For example, in the exothermic reaction between zinc and aqueous copper sulfate some of the heat produced in the reaction is lost to the environment, so the maximum temperature recorded is lower than the true valued obtained in a perfectly insulated system. We can make some allowance for the heat loss by extrapolating the cooling section of the graph to the time when the reaction started. 1857 Isa

Enthalpy Changes of Reaction in Solution Example 50.0 cm3 of 0.200 mol dm-3 copper(II) sulfate solution was placed in a polystyrene cup. After two minutes 1.20 g of powdered zinc was added. The temperature was taken every 30 seconds. Calculate the enthalpy change for the reaction taking place. Step 1- write the net ionic equation for the reaction: Cu2+(aq) + Zn(s)  Cu(s) + Zn2+(aq) Step 2 – determine the limiting reactant Amount of Cu2+(aq) = 50.0/1000 x 0.200 = 0.0100 mol Amount of Zn(s) = 1.20/65.37 = 0.0184 mol

Enthalpy Changes of Reaction in Solution Step 3- extrapolate the graph to compensate for heat loss and determine Δ T. In this case, ΔT= 55.0 oC Step 4 – Calculate the heat evolved in the experiment for 0.0100 mol of reactants Heat evolved = 50.0 x 4.184 x 55.0/1000 = 11.5 kJ Step 5 – Express this as the enthalpy change for the reaction, Δ H = -11.5 kJ/0.0100 = -1150 kJ mol-1

Enthalpy Changes of Reaction in Solution

Heat of Combustion The heat produced when one mole of a substance is burned in oxygen is called the enthalpy change of combustion. When the heat released by exothermic reaction is absorbed by water, the temperature of water increases, so the heat produced by the reaction can be calculated if it is assumed that all the heat is absorbed by the water. Heat change of reaction = heat change of water Heat rxn = mH2O · sH2O · ΔTH2O

Heat of Combustion In an exothermic reaction, the heat produced by the reaction is absorbed by the water so its temperature increases and the heat change is negative. In an endothermic reaction, the heat absorbed by the reaction is taken from the water so its temperature decreases and the heat change is positive. Since the heat changed observed depends on the amount of reaction, enthalpy changes are usually expressed in kJ mol-1

Heat of Combustion

Heat of Combustion Example Calculate the enthalpy of combustion of ethanol from the following data. Assume all the heat from the reaction is absorbed by the water. Compare your answer with the IB Data booklet and suggest reasons for any differences. Mass of water in copper calorimeter (g) 200.00 Temperature increase in water (oC) 13.00 Mass of ethanol burned (g) 0.45

Heat of Combustion Solution 1st – calculate the heat released by the reaction. Heat rxn = mH2O · sH2O · ΔTH2O Heat rxn = 200.00 · 4.184 · 13.00 = -10880 J -10880 J = -10.88 kJ 2nd – divide the heat released by the number of moles to express the enthalpy change in kJ mol-1 Number of moles of C2H5OH = mass of C2H5OH molar mass of C2H5OH Moles of C2H5OH = 0.45 g C2H5OH/46.08 g mol-1 = 0.0098 moles -10.88 kJ/0.0098 mol = -1100 kJ mol-1

Heat of Combustion Solution (cont’d) The IB Data booklet value is – 1371 kJ mol-1 . Suggested reasons for the difference: Not all the heat produced by the combustions is transferred to the water. Some heat is absorbed by the calorimeter and some has passed to the surroundings. The combustion of the ethanol is not complete due to insufficient oxygen supply.

Enthalpy Changes of Reaction in Solution For an exothermic reaction, Δ Hreaction is negative as heat has passed from the reaction into the water. Heat rxn = mH2O · sH2O · ΔTH2O In order to determine the molar enthalpy change for the reaction, the limiting reactant must be identified. The molar heat change of reaction = Heat rxn moles of limiting reactant